Related papers: Topological Dynamics of Groupoid Actions
Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids
Our aim is to find some new links between linear (circular) orderability of groups and topological dynamics. We suggest natural analogs of the concept of algebraic orderability for topological groups involving order-preserving actions on…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
In this paper we investigate some connections between Topological Dynamics, the theory of G-Principal Bundles, and the theory of Locally Trivial Groupoids.
Some boundedness properties of function spaces (considered as topological groups) are studied.
We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a…
We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact…
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various…
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
Topologically and geometrically engaging actions have proved to be useful to obtain rigidity results for semisimple Lie group actions. We show that the action of a simple noncompact Lie group on a compact manifold preserving a unimodular…
In analogy with the classical theory of topological groups, for finitely complete categories enriched with Grothendieck topologies, we provide the concepts of localized G-topological space, initial Grothendieck topologies and continuous…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
We have defined and established a theory of cofinite connectedness of a cofinite graph. Many of the properties of connectedness of topological spaces have analogs for cofinite connectedness. We have seen that if $G$ is a cofinite group and…
We define the action of a locally compact group $G$ on a topological graph $E$. This action induces a natural action of $G$ on the $C^*$-correspondence ${\mathcal H}(E)$ and on the graph $C^*$-algebra $C^*(E)$. If the action is free and…
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between…
Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.
Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that…